GLOBAL ATTRACTOR FOR A DENSITY-DEPENDENT SENSITIVITY CHEMOTAXIS MODEL

doi:10.1016/S0252-9602(12)60105-2

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (4): 1365-1375.doi: 10.1016/S0252-9602(12)60105-2

GLOBAL ATTRACTOR FOR A DENSITY-DEPENDENT SENSITIVITY CHEMOTAXIS MODEL

陈学勇^1,2|刘伟安¹

1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;
2. School of Mathematics and Statistics, Xuchang University, Xuchang 461000, China

收稿日期:2010-12-30 修回日期:2011-06-21 出版日期:2012-07-20 发布日期:2012-07-20
基金资助:
Supported by National Natural Science Foundation of China (10871151).

GLOBAL ATTRACTOR FOR A DENSITY-DEPENDENT SENSITIVITY CHEMOTAXIS MODEL

CHEN Xue-Yong^1,2, LIU Wei-An¹

1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;
2. School of Mathematics and Statistics, Xuchang University, Xuchang 461000, China

Received:2010-12-30 Revised:2011-06-21 Online:2012-07-20 Published:2012-07-20
Supported by:
Supported by National Natural Science Foundation of China (10871151).

摘要/Abstract

摘要：

In this paper, a chemotaxis model with reproduction term in a bounded do-main Ω( Rⁿ is discussed. The existence of a global-in-time solution and a global attractor for this model are obtained.

关键词: chemotaxis, global existence, global attractor

Abstract:

In this paper, a chemotaxis model with reproduction term in a bounded do-main Ω( Rⁿ is discussed. The existence of a global-in-time solution and a global attractor for this model are obtained.

Key words: chemotaxis, global existence, global attractor

中图分类号:

35L50

陈学勇, 刘伟安. GLOBAL ATTRACTOR FOR A DENSITY-DEPENDENT SENSITIVITY CHEMOTAXIS MODEL[J]. 数学物理学报(英文版), 2012, 32(4): 1365-1375.

CHEN Xue-Yong, LIU Wei-An. GLOBAL ATTRACTOR FOR A DENSITY-DEPENDENT SENSITIVITY CHEMOTAXIS MODEL[J]. Acta mathematica scientia,Series B, 2012, 32(4): 1365-1375.

[1] Keller E F, Segel L A. Initiation of slime mould aggregation viewed as an instability. J Theoret Biol, 1970, 26: 399–415

[2] Hale J K. Asymptotic Behaviour of Dissipative Systems. Providence, RI: Amer Math Soc, 1988

[3] Babin A V, Vishik M I. Attractors of partial differential evolution equations in an unbounded domain. Proc R Soc Edinb. 1990, 116A: 221–243

[4] Ladyzhenskaya O. Attractors for Semigroups and Evolutions. Cambridge: Cambridge University Press, 1991

[5] Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. New York: Springer-Verlag, 1983

[6] MarionM. Finite-dimensional attractors associated with partly dissipative reaction-diffusion system. SIAM J Math Anal, 1989, 20: 816–844

[7] Anibal R B, Wang B X. Attractors for partly dissipative reaction diffusion system in Rn. J Math Anal Appl, 2000, 252: 790–803

[8] Friedman A. Partial Differential Equations. New York: Holt Rinehart and Winston, 1969

[9] Mora X. Semilinear parabolic problems define semiflows on Ck spaces. Trans Amer Math Soc, 1983, 278: 21–55

[10] Osaki K, Tsujikawa T, Yagi A. Exponential attractor for a chemotaxis-growth system of equatons. Non-linear Anal, 2002, 51: 119–144

[11] Wang B X. Attractors for reaction diffusion equations in unbounded domain. Phys D, 1999, 128: 41–52

[12] Horstmann D, Winkler M. Boundedness vs blow-up in a chemotaxis system. J Diff Eqns, 2005, 215: 52–107

[13] Naigai T, Syukuinn R, Umesako M. Decay properties and asymptotic profiles of bounded solutions to a parabolic system of chemotaxis in Rn. Funkcialaj Ekvacioj, 2003, 46: 383–407

[14] Ladyzhenskaja O A, Solonnikov V A, Uraltseva N N. Linear and Quasi-linear Equations of Parabolic Type. Providence, RI: Amer Math Soc, 1968

[15] Li Junfeng, Liu Weian. Existence of solution to some Othmer-Stevens chemotaxis system with reaction term. Acta Mathematica Scientia, 2009, 29A(6): 1561–1571

[16] Zhong Xinhua, Jiang Song. Globally bounded in-time solutions to a parabolic-elliptic system modelling chemotaxis. Acta Mathematica Scientia, 2007, 27B(2): 421–429

GLOBAL ATTRACTOR FOR A DENSITY-DEPENDENT SENSITIVITY CHEMOTAXIS MODEL

GLOBAL ATTRACTOR FOR A DENSITY-DEPENDENT SENSITIVITY CHEMOTAXIS MODEL

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